BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

How to tell if a number is divisible by 7?

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Senior | Next Rank: 100 Posts
Posts: 90
Joined: Mon May 02, 2011 11:18 am
Location: Florida
Thanked: 20 times
Followed by:7 members
GMAT Score:710

How to tell if a number is divisible by 7?

by rishimaharaj » Wed Jun 29, 2011 6:15 am
Hi all,
I posted this on my blog [https://dudewheysmehblog.blocked/20 ... -by-7.html] and wanted to share it here also.

The test prep books I've seen so far all say that you can only find if a number is divisible by 7 through long division (Manhattan GMAT, Number Properties - updated for 12th Edition - page 14).

The source I'm quoting from was given to me by my wife. She got the book in India:
The Pearson Guide to Objective Arithmetic (for competitive examinations) First Edition. You can find the Third Edition here: https://amegabooks.com/competitive-exams ... 40713.html

On pages 4 and 5, it breaks down the divisibility of numbers by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 25, 125, 18, and 88.

Here is what it says for Divisibility by 7:
The unit digit of the given number is doubled and then it is subtracted from the number obtained after omitting the unit digit. If the remainder is divisible by 7, then the given number is also divisible by 7.
For example, consider 448. On doubling the unit digit of 8, we get 16.
Then, 44 - 16 = 28.
Since 28 is divisible by 7, 448 is divisible by 7.
The cool thing about this is that you can repeat the steps over and over again until you get your answer. For example, take the number 3,752.
  1. Separating the units digit, we get two numbers: 375 and 2.
    1. 2 doubled is 4.
    2. 375 - 4 = 371
  2. Separating the units digit, we get two numbers: 37 and 1.
    1. 1 doubled is 2.
    2. 37 - 2 = 35.
    3. We can stop here since we know 7 * 5 = 35, but if we want to, we can keep going.
  3. Separating the units digit, we get 3 and 5.
    1. 5 doubled is 10.
    2. 3 - 10 = -7, which is divisible by 7.
Hope this helps!
All the best in your GMAT preparation!
--Rishi
Top
Source: — Quantitative Reasoning |
Legendary Member
Posts: 1448
Joined: Tue May 17, 2011 9:55 am
Location: India
Thanked: 375 times
Followed by:53 members

by Frankenstein » Wed Jun 29, 2011 6:27 am
Hi,
Appreciate your work. In fact, similar rules can be framed for divisibility rules of other primes as well.
For example, you can add double of unit digit to the rest of the number and check if it is divisible by 19.
consider 399
39 + 2*9 = 57(divisible by 19). So, 399 is divisible by 19. Although I am not sure these things will help us in GMAT or not. Some people feel ordinary division is easier. Anyway good work!
Cheers!

Things are not what they appear to be... nor are they otherwise
Top
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pm
Location: Gandhinagar
Thanked: 41 times
Followed by:2 members

by shashank.ism » Wed Jun 29, 2011 12:15 pm
Taking into consideration "Divisibility by 7", I have posted a similar steps on my blog-post. https://mba.webmaggu.com/divisibility-by-7/

Though checking divisibility by this method is quite repetitive and cumbersome. So I would better recommend to divide the number simply by 7 and get the result. :)
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Wed Jun 29, 2011 2:07 pm
rishimaharaj wrote:

Here is what it says for Divisibility by 7:
The unit digit of the given number is doubled and then it is subtracted from the number obtained after omitting the unit digit. If the remainder is divisible by 7, then the given number is also divisible by 7.
For example, consider 448. On doubling the unit digit of 8, we get 16.
Then, 44 - 16 = 28.
Since 28 is divisible by 7, 448 is divisible by 7.
The cool thing about this is that you can repeat the steps over and over again until you get your answer. For example, take the number 3,752.
  1. Separating the units digit, we get two numbers: 375 and 2.
    1. 2 doubled is 4.
    2. 375 - 4 = 371
  2. Separating the units digit, we get two numbers: 37 and 1.
    1. 1 doubled is 2.
    2. 37 - 2 = 35.
    3. We can stop here since we know 7 * 5 = 35, but if we want to, we can keep going.
  3. Separating the units digit, we get 3 and 5.
    1. 5 doubled is 10.
    2. 3 - 10 = -7, which is divisible by 7.
There are divisibility 'tricks' for all kinds of numbers, but many of them are awkward to apply. The only ones I've ever found useful on GMAT questions are the 'tricks' for 2, 3, 5 and multiples of those primes (4, 9, 10, etc).

While there is certainly no harm in knowing a 'trick' for divisibility by 7, I'd point out two things:

* you won't ever need to check, on the GMAT, whether some six-digit number is divisible by 7, so there isn't any great value in knowing 'tricks' for 7. You may, however, need to check if a longer number is divisible by 3 or 9, so those tests are useful (e.g. in Q16 in the DS section of the green Quant Review book).

* If I want to know whether 448 is divisible by 7, I'd just locate a 'simple' multiple of 7 close to 448, and work out whether the difference is divisible by 7. Since 448 is 28 more than 420, 448 must be divisible by 7. Notice the advantage here: I not only get an answer to the question, I also find the quotient in the process. Since 448 = 420 + 28 = 7(60 + 4), I know that 448 = 7*64. Similarly, if I want to know if 3752 is divisible by 7, I can just take away easy multiples of 7:

3752 = 3500 + 252 = 3500 + 210 + 42 = 7*(500 + 30 + 6) = 7*536

I personally would find that faster than applying the divisibility 'trick' for 7.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pm
Location: Gandhinagar
Thanked: 41 times
Followed by:2 members

by shashank.ism » Thu Jun 30, 2011 2:47 am
Ian, that was a nice post of yours..
Practically, the divisibility test by 2,3,5 only works when we solve a problem. We feel tough to use other methods or either forget the exact method.

Moreover questions in GMAT are quite simple and it doesn't require such tricks every now and then.

The method you have given in the second point is great. I mean people do this thing but if they follow it regularly it will surely help to solve the problems out. And method would work with all numbers atleast for smaller ones.

Great post...
Inspired by your method I posted a new topic "A small Divisibility Trick for any number" https://mba.webmaggu.com/a-small-divisib ... ny-number/ in my blog, so that more people can read it and try such a small but uselful tip. :)
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 90
Joined: Mon May 02, 2011 11:18 am
Location: Florida
Thanked: 20 times
Followed by:7 members
GMAT Score:710

by rishimaharaj » Thu Jun 30, 2011 5:37 am
Ian Stewart wrote: * If I want to know whether 448 is divisible by 7, I'd just locate a 'simple' multiple of 7 close to 448, and work out whether the difference is divisible by 7. Since 448 is 28 more than 420, 448 must be divisible by 7. Notice the advantage here: I not only get an answer to the question, I also find the quotient in the process. Since 448 = 420 + 28 = 7(60 + 4), I know that 448 = 7*64. Similarly, if I want to know if 3752 is divisible by 7, I can just take away easy multiples of 7:

3752 = 3500 + 252 = 3500 + 210 + 42 = 7*(500 + 30 + 6) = 7*536
Ian,
That's a very simple and elegant solution! It's easy, efficient, makes sense, and gives the quotient!
Many thanks for sharing!
--Rishi
Top
Post new topic Post Reply
• Page 1 of 1